### Abstract

Abstract A recently developed multigrid method (Botto, 2013), based on the concept of volume fraction, has been tested for the inversion of the Helmholz-type equation for the free surface in the environmental public domain code COHERENS. The volume fraction concept is particularly interesting for coarse grid cells that are agglomerated from both dry and wet fine grid cells at irregular coastlines. At these locations, modifying the prolongation operator and the coarse grid discretization, using the volume fraction, results in better convergence. However, as convergence deteriorates in the case of small, elongated islands that tend to disappear by the multigrid coarsening procedure, a correction is proposed, yielding good convergence rates, irrespective of the presence of small or large islands. The method is tested extensively for the inversion of the academic Poisson equation. Larger test cases, solving the Helmholz-type equation, prove the applicability for real-life applications of environmental flows.

Original language | English (US) |
---|---|

Article number | 10084 |

Pages (from-to) | 22-36 |

Number of pages | 15 |

Journal | Journal of Computational and Applied Mathematics |

Volume | 289 |

DOIs | |

State | Published - Jun 3 2015 |

Externally published | Yes |

### Fingerprint

### Keywords

- Helmholz equation
- Multigrid
- Poisson equation
- Shallow water flow
- Small island problem
- Stair-case boundary

### ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics

### Cite this

*Journal of Computational and Applied Mathematics*,

*289*, 22-36. [10084]. https://doi.org/10.1016/j.cam.2015.03.029

**A geometric multigrid solver for the free-surface equation in environmental models featuring irregular coastlines.** / Rauwoens, Pieter; Troch, Peter A; Vierendeels, Jan.

Research output: Contribution to journal › Article

*Journal of Computational and Applied Mathematics*, vol. 289, 10084, pp. 22-36. https://doi.org/10.1016/j.cam.2015.03.029

}

TY - JOUR

T1 - A geometric multigrid solver for the free-surface equation in environmental models featuring irregular coastlines

AU - Rauwoens, Pieter

AU - Troch, Peter A

AU - Vierendeels, Jan

PY - 2015/6/3

Y1 - 2015/6/3

N2 - Abstract A recently developed multigrid method (Botto, 2013), based on the concept of volume fraction, has been tested for the inversion of the Helmholz-type equation for the free surface in the environmental public domain code COHERENS. The volume fraction concept is particularly interesting for coarse grid cells that are agglomerated from both dry and wet fine grid cells at irregular coastlines. At these locations, modifying the prolongation operator and the coarse grid discretization, using the volume fraction, results in better convergence. However, as convergence deteriorates in the case of small, elongated islands that tend to disappear by the multigrid coarsening procedure, a correction is proposed, yielding good convergence rates, irrespective of the presence of small or large islands. The method is tested extensively for the inversion of the academic Poisson equation. Larger test cases, solving the Helmholz-type equation, prove the applicability for real-life applications of environmental flows.

AB - Abstract A recently developed multigrid method (Botto, 2013), based on the concept of volume fraction, has been tested for the inversion of the Helmholz-type equation for the free surface in the environmental public domain code COHERENS. The volume fraction concept is particularly interesting for coarse grid cells that are agglomerated from both dry and wet fine grid cells at irregular coastlines. At these locations, modifying the prolongation operator and the coarse grid discretization, using the volume fraction, results in better convergence. However, as convergence deteriorates in the case of small, elongated islands that tend to disappear by the multigrid coarsening procedure, a correction is proposed, yielding good convergence rates, irrespective of the presence of small or large islands. The method is tested extensively for the inversion of the academic Poisson equation. Larger test cases, solving the Helmholz-type equation, prove the applicability for real-life applications of environmental flows.

KW - Helmholz equation

KW - Multigrid

KW - Poisson equation

KW - Shallow water flow

KW - Small island problem

KW - Stair-case boundary

UR - http://www.scopus.com/inward/record.url?scp=84930277002&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84930277002&partnerID=8YFLogxK

U2 - 10.1016/j.cam.2015.03.029

DO - 10.1016/j.cam.2015.03.029

M3 - Article

AN - SCOPUS:84930277002

VL - 289

SP - 22

EP - 36

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

M1 - 10084

ER -